Nonlinear Dynamics in a Chemical Reaction under an Amplitude-Modulated Excitation: Hysteresis, Vibrational Resonance, Multistability, and Chaos

Monwanou, A. V.; Koukpémèdji, A. A.; Ainamon, Cyrille; Tuwa, P.R. Nwagoum; Miwadinou, C. H.; Orou, J. B. Chabi

doi:10.1155/2020/8823458

Cited by 16 publications

(12 citation statements)

References 20 publications

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“…To verify these analytical results, we have numerically studied the real and imaginary parts of the eigenvalues σ when c 1 varies from −1 to 11. By using the polynomial companion matrix and the standard eignvalue solver Lapack [46][47][48][49][50][51][52], the obtained results are shown in figure 2. From the analysis of this figure, we note that when −1 c 1 11, the zero eigenvalue still exists.…”

Section: Fixed Point Stability Analysismentioning

confidence: 99%

Effect of biharmonic excitation on complex dynamics of a two-degree-of-freedom heavy symmetric gyroscope

Aguessivognon,

Miwadinou,

Monwanou

2023

Phys. Scr.

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This work analyzes the chaotic dynamics and the coexistence of attractors and their control in the complex dynamics of a rotating gyroscope modeled following Euler angles using the Lagrange approach. The fixed points of the system is checked and their stability analyzed. The complete dynamics of the gyroscope is studied and the coexistence of attractors analyzed using Runge-Kutta algorithm of order 4. It is obtained for appropriate conditions the coexistence of chaotic and/or regular attractors. The study also pointed out that the dissipation and the first integrals of the moments of inertia of the gyroscope influence the chaotic dynamics as well as the coexistence of the attractors. Finally, the control of the coexistence of attractocs obtained is done using a biharmonic excitation. The analysis of the effects of the amplitudes and frequencies of this excitation makes it possible to find the best areas where the control is effective.

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Section: Fixed Point Stability Analysismentioning

confidence: 99%

Effect of biharmonic excitation on complex dynamics of a two-degree-of-freedom heavy symmetric gyroscope

Aguessivognon,

Miwadinou,

Monwanou

2023

Phys. Scr.

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“…where p � ω 2 0 (F 1 α 1 − η)/(ηc) and q � ω 2 0 (F 1 α 0 − F 0 η)/ (ηc). e roots of equation ( 9) can be derived as [46,62]…”

Section: Equilibrium Stability and Its Evolutionsmentioning

confidence: 99%

“…)/2. According to Cardan discriminant [46,62], when Δ ≻ 0, one positive real equilibrium point is obtained from (11), since the equilibrium point cannot be a complex number. us, the system possesses in this case, one Hopf bifurcation point (HBP).…”

Section: Equilibrium Stability and Its Evolutionsmentioning

confidence: 99%

Chaotic Dynamics of a Mixed Rayleigh–Liénard Oscillator Driven by Parametric Periodic Damping and External Excitations

et al. 2021

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In this paper, chaotic dynamics of a mixed Rayleigh–Liénard oscillator driven by parametric periodic damping and external excitations is investigated analytically and numerically. The equilibrium points and their stability evolutions are analytically analyzed, and the transitions of dynamical behaviors are explored in detail. Furthermore, from the Melnikov method, the analytical criterion for the appearance of the homoclinic chaos is derived. Analytical prediction is tested against numerical simulations based on the basin of attraction of initial conditions. As a result, it is found that for ω = ν , the chaotic region decreases and disappears when the amplitude of the parametric periodic damping excitation increases. Moreover, increasing of F 1 and F 0 provokes an erosion of the basin of attraction and a modification of the geometrical shape of the chaotic attractors. For ω ≠ ν and η = 0.8 , the fractality of the basin of attraction increases as the amplitude of the external periodic excitation and constant term increase. Bifurcation structures of our system are performed through the fourth-order Runge–Kutta ode 45 algorithm. It is found that the system displays a remarkable route to chaos. It is also found that the system exhibits monostable and bistable oscillations as well as the phenomenon of coexistence of attractors.

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“…In order to validate the analytical predictions, we have simulated numerically the set of Eqs. ( 25) and (26) to see the effects of the control parameters on the fractality of the basin of attraction. To this end, the obtained results are presented in Fig.…”

Section: Active Control 51 Effects Of the Control On The Horseshoe Chaosmentioning

confidence: 99%

“…It belongs to a category of nonlinear chemical reactions well developed in the scientific literature. We made this choice because it has already been demonstrated that a modified Van der Pol-Duffing oscillator can be used to model the nonlinear chemical oscillations like BZ reactions [21][22][23][24][25][26]. Since the control of regular and irregular motions is an interesting issue in several areas [27], the dynamical behavior of a forced generalized Rayleigh oscillator, which constitutes a new model for describing the nonlinear chemical oscillations, may be investigated.…”

Section: Introductionmentioning

confidence: 99%

Dynamics and active control of chemical oscillations modeled as a forced generalized Rayleigh oscillator with asymmetric potential

Joseph¹,

Fernando²,

Clément³

et al. 2021

IJBAS

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This paper focuses on the dynamics and active control of chemical oscillations governed by a forced generalized Rayleigh oscillator. The Melnikov method is used to analytically determine the critical parameters for the onset of chaotic motions. The analytical results are confirmed by numerical simulations. The bifurcation structures obtained show that the model displays a rich variety of dynamical behaviors and remarkable routes to chaos. The effects of the control gain parameters on the behavior of the system are analyzed and the results obtained have shown the control efficiency.

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Nonlinear Dynamics in a Chemical Reaction under an Amplitude-Modulated Excitation: Hysteresis, Vibrational Resonance, Multistability, and Chaos

Cited by 16 publications

References 20 publications

Effect of biharmonic excitation on complex dynamics of a two-degree-of-freedom heavy symmetric gyroscope

Effect of biharmonic excitation on complex dynamics of a two-degree-of-freedom heavy symmetric gyroscope

Chaotic Dynamics of a Mixed Rayleigh–Liénard Oscillator Driven by Parametric Periodic Damping and External Excitations

Dynamics and active control of chemical oscillations modeled as a forced generalized Rayleigh oscillator with asymmetric potential

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